Hey Katie!
Wishes Nighttime Spectacular is the fireworks show which is put on almost nightly.
On select dates in November and December, Mickey's Very Merry Christmas Party (MVMCP) takes over Magic Kingdom Park. This is a separately ticketed event. Magic Kingdom Park will close around 7pm to guests who do not have MVMCP tickets. On MVMCP nights, Wishes Nighttime Spectacular is not shown. Instead, guests attending the party are treated to Holiday Wishes: Celebrate the Spirit of the Season, which is a holiday-themed version of the original Wishes. It's truly breathtaking.
MVMCP typically ends the week of Christmas. At that time, all guests are treated to both the Holiday Wishes show and the Mickey's Once Upon A Christmastime Parade as part of standard park admission.
The Tomorrowland Terrace Fireworks Desert Party has been offered on MVMCP nights. In order to gain access to the Desert Party, you would also have to have admission to MVMCP as well as pay for admission to the Desert Party.
I hope this answers your questions, Katie! Please come back and see me if you have any others. We love visiting Walt Disney World during the holidays!
Have a magical day!
Ashley